06 Nov Momentum Investing

Early Works of Momentum Investing

Many practitioners had successfully implemented Momentum investing with some prominent names dating back more than a century.

One such prominent figure is classical economist David Ricardo. His concept of “cut short your losses” and “let your profits run on” in 1838 is absolute momentum investing in nature.

Jesse Livermore had stated clearly that the “big money was not in the individual fluctuations but in … sizing up the entire market and its trend.” This is also suggestive of absolute momentum investing in play.

In the 1920s, Richard Wyckoff advocated buying the strongest stocks within the strongest sectors and within the strongest index when they were trending up.

In 1939, George Seamans advocated buying stronger stocks during an advance and sell weaker stocks during a decline, in his book “The Seven Pillars of Stock Market Success”.

Defining Momentum

“Momentum” has different meaning to different market participants. It is important to clearly define some commonly used terms related to momentum.

Academics and some practitioners have generally been referring to momentum to mean that within a specified market, the winners continue to win and losers continue to lose. In other words, winners outperform losers. This is also called relative momentum, cross-sectional momentum or relative strength.

“Momentum” can also mean that a security/market with recent positive returns continue to move higher while recent negative returns continue to move lower. This is also called trend following, absolute momentum or time series momentum.

Basics of Absolute Momentum

“Momentum” has different meaning to different people.

“Absolute momentum” is also known as “trend following” or “time series momentum”

Basics of Relative Momentum

“Relative momentum” is also known as “cross-sectional momentum” or “relative strength”.

Relative momentum means that within a specified market, the winners continue to win and losers continue to lose. In other words, winners outperform losers.

Put in another way,

Momentum is the tendency of investments to exhibit persistence in their relative performance. Investments that have performed relatively well, continue to perform relatively well; those that have performed relatively poorly, continue to perform relatively poorly. – AQR

Nobel Prize Winner Eugene Fama and Kenneth French, who are accepted as Fathers of Efficient Market Hypothesis, describe the persistence of Momentum as:

The premier market anomaly is momentum. Stocks with low returns over the past year tend to have low returns for the next few months, and stocks with high past returns tend to have high future returns.

Historical Profitability of Absolute Momentum For Last Few Decades

Absolute Momentum has been profitable generally since 1985 for various asset classes such as equity index futures, fixed income futures, commodity futures and currency forwards. Absolute Momentum strategy explains the strong performance of Managed Futures funds from the late 1980s. – AQR

Wellington Management’s paper showed that a simple moving average timing method applied to S&P 500 improved risk adjusted returns. This is shown in “Figure 2” of the paper, reproduced below.

Source: Wellington Management

Furthermore AQR finds:

strong positive predictability from a security’s own past returns for almost five dozen diverse futures and forward contracts that include country equity indexes, currencies, commodities, and sovereign bonds over more than 25 years of data. They find that the past 12-month excess return of each instrument is a positive predictor of its future return. This time series momentum or ‘‘trend’’ effect persists for about a year and then partially reverses over longer horizons. These findings are robust across a number of subsamples, look-back periods, and holding periods.

They find that 12-month time series momentum profits are positive, not just on average across these assets, but for every asset contract examine (58 in total). Their finding of positive time series momentum that partially reverse over the long-term may be consistent with initial under-reaction and delayed over-reaction, which theories of sentiment suggest can produce these return patterns

The existence and significance of time series momentum is robust across horizons and asset classes, particularly when the look-back and holding periods are 12 months or less. In addition, they confirm that the time series momentum results are almost identical if they use the cash indexes for the stock index futures.

“The Case for Momentum Investing” shows that relative momentum exists in a range of global asset classes and markets in “Exhibit 2” of the paper, reproduced below.

Source: AQR Capital Management

Relative Momentum on Individual Stocks

Investors can check for fundamental support for the recent price action of a company’s stock. One commonly used metric to measure a firm’s business strength is earnings momentum which suggests improving revenues and/or better profit margins. In a Columbia Threadneedle article: “Looking for sustainable momentum”, it is shown that among the top 20% of price momentum stocks, higher ranked earnings momentum stocks outperforms lower ranked stocks. This is shown in “Exhibit 4” of the article, reproduced below.

Source: Columbia Threadneedle Investments

AQR’s “The Case for Momentum Investing” shows that stocks with the best momentum outperform the ones with the worst momentum, both in absolute terms and relative to the equity market as a whole. See “Exhibit 1” of the paper, reproduced below.

Source: AQR Capital Management

“Momentum investing in Asia” shows that Relative Momentum effect is evident in Asia, with both price and earnings momentum factors delivering positive alpha over the period of analysis.

Asian stocks exhibited the price momentum effect over the 3 to 12 month horizon, with the past 12-month price momentum factor performing the best. It was also observed that a short-term reversal effect (in contrast to momentum) was seen in Asia over the 1 month horizon; the past 1-month outperformers subsequently underperformed the broader market whereas the past 1-month laggards subsequently outperformed. We could enhance the effectiveness of momentum factors by excluding the impacts of the reversal effect.

“Exhibit 1” of the paper (reproduced below) shows the momentum effect of both price and earnings in Asia stocks.

Source: Asiya Investments

Relative Momentum on Currencies

Relative momentum has been typically applied to Equities. BT Funds Management applied the same approach to Currencies. Results show that buying the most attractive currency and selling the least attractive currency obtains average excess returns that are significantly positive.

To consider diversification, we can explicitly construct a spectrum of portfolios we would invest in, and run our momentum model on the portfolios to determine a point in time allocation. This parallels the methodology of taking a universe of stocks and investing based on a momentum screen or score but here we are treating each individual portfolio as a single asset. Treating each portfolio as if they are their own asset class allows us to capture the effects of diversification without the momentum selection process.

The static portfolio provides the diversification while the momentum framework focuses on the behaviour of the portfolios as individual assets.

To build the diversified strategy we first construct 4 static portfolios consisting of a US Equity/Treasury allocation of 80%/20%, 60%/40%, 40%/60% and 20%/80% rebalanced on an annual basis. We add a 100% US Equity and 100% Treasuries option to complete a 6 choice spectrum of investments for the strategy. As before the strategy will on a monthly basis invest in the allocation option that has the greatest trailing one year Sharpe ratio.

As noted in the table below, the Diversified strategy showed an improvement in both total and risk adjusted return compared to the simple Sharpe switching strategy over the period (1977-2014).

Source: Newfound Research

Next the paper selected 4 S&P Target Risk indexes which comprise a common global risk spectrum for portfolios. The MSCI All Country World Index and Barclays 1-3 year US Treasury Index is added to complete a 6 option portfolio spectrum.

The same process using 6 and 12 months lookback produced results below.

Mebane Faber’s paper explores investing in sectors based on Relative Momentum. The paper explores various permutations, investing in the top 1, 2, 3, up to 9 sectors on equal weighted basis. Relative Momentum method works on all of the measurement periods from one month to twelve months, as well as a combination of the 1, 3, 6, 9, and 12 month time periods. As investing in Equities Sectors is inherently high risk with high max drawdowns, the resulting performance of a Relative Momentum strategy on Equities sectors also displays high max drawdowns.

The paper: “Using Style Index Momentum to Generate Alpha” explores Relative Momentum on Style Indexes. Indexes used are the Russell 2000 Growth, Russell 2000 Value, Russell Mid-Cap Growth, Russell Mid-Cap Value, Russell Top 200 Growth, Russell Top 200 Value. They analyze various formation periods to rank each of the six indexes based on their return over that period of time. For each index held they then calculated subsequent returns for various holding periods. An example would be a 24,6 portfolio, which means they ranked the style indexes based on 24 month prior performance, then held each single style index portfolio for 6 months based on its formation period performance. They rank the style indexes based on formation period performance, then buy the top performing index and short the bottom performing index.

Results are generally positive and statistically significant, especially for the shorter holding periods. Long-Short returns across various formation periods peak at 12 months of prior performance. Across various holding periods the Long-Short returns peak at 1 month. This is shown in “Exhibit 1” of the paper, reproduced below.

Source: Using Style Index Momentum to Generate Alpha

Absolute Momentum on Individual Stocks

Absolute momentum has traditionally been applied to futures markets due to the uncorrelated nature of different asset classes and markets available for trading in futures.

Equities on the other hand tend to be highly correlated, especially during crisis periods. This is the biggest problem with traditional trend following applied on individual stocks. Diversification is key to success of any traditional trend following strategy and trading individual stocks doesn’t offer sufficient diversification.

Andreas Clenow shows in his book that a traditional trend following which worked well for futures trading simply didn’t work on individual stocks.

Apart from issues with lack of diversification, shorting individual stocks poses another major problem.

Driehaus Capital Management explains their investing approach in an article “Momentum Investing in US Smaller Cap Equities“. Their approach is rooted in the belief that earnings drive stock prices. They look for companies where future earnings growth is either underestimated or overly discounted. This often results in accelerating earnings growth when a company is in the early stages of positive fundamental change. Fundamental momentum then drives technical momentum. Accelerating EPS and valuation expansion can result in significant stock price appreciation.

A stock is considered to have fundamental momentum when the below are present:

Positive estimate revisions

Accelerating growth rates – where revenue and/or earnings per share is growing at an increasing rate from one period to the next

Positive revenue and earnings surprises

Improving operating metrics (e.g. backlog, orders, etc.)

A stock is considered to have technical momentum when the below are present:

Rising stock price

Rising moving average

Rising relative strength

Increasing trading volume

Positive exposure to medium term momentum (cumulative return over the past 250 trading days, excluding the last 20 trading days)

Longboard’s paper: “Does Trend Following Work on Stocks?” tested a trend following approach on individual stocks. They used all time highest close as the entry method to determine trend. For exit, they used 10x 45 day Average True Range trailing stops because they are universally applicable and commonly used by trend following programs. The evidence suggests that trend following can work well on stocks. Buying stocks at new all time highs and exiting them after they’ve fallen below an ATR trailing stop would have yielded a significant return on average. This is shown in the table from the paper (reproduced below).

Source: Longboard Asset Management

Absolute Momentum for Asset Allocation

Due to Absolute Momentum strategy’s ability to perform well during extreme events and it’s low correlation to stocks and bonds, allocation to Absolute Momentum strategy would improve the performance of a traditional portfolio.

“Exhibit 4” from AQR’s paper (reproduced below) shows the simulated effect of allocating 20% of the capital from a 60/40 traditional portfolio to the Absolute Momentum strategy. We see that such an allocation reduces the maximum portfolio drawdown, lowers portfolio volatility and increases portfolio returns.

The 60/40 portfolio without momentum shows some reduction in volatility and drawdown compared to an investment solely in US stocks. However, the strong 0.92 monthly correlation of the 60/40 portfolio with the S&P 500 shows that the 60/40 portfolio has retained most of the market risk of stocks. Because stocks are much more volatile than bonds, stock market movement dominates the risk in a 60/40 portfolio. From a risk perspective, the regular 60/40 portfolio is, in fact, mostly an equity portfolio, since stock market variation explains most of the variation in performance of the 60/40 portfolio.

The MSCI US index with the addition of absolute momentum has a 0.74 correlation to the S&P 500, which is lower than the 0.92 correlation of the 60/40 index to the S&P 500. MSCI US with absolute momentum does a better job than the 60/40 portfolio in reducing portfolio drawdown, while also providing higher returns. The correlation to the S&P 500 of the 60/40 portfolio using 12-month absolute momentum drops to 0.67 from 0.92.6 The 60/40 portfolio with absolute momentum retains the same return as the normal MSCI US Index, but with only half the volatility. The maximum drawdown drops by more than 70%.

See details in “Table 4” of the paper, reproduced below.

Source: Gary Antonacci

Parity with 12-month absolute momentum, as presented here, is more adaptive than normal risk parity and has the ability to exit fixed income investments during periods of rising interest rates due to its trend following nature.

See details in “Table 6” of the paper, reproduced below.

Source: Gary Antonacci

Mebane Faber’s paper explores a quantitative market timing approach that manages risk of the portfolio on top of traditional risk reduction from diversification. The approach signals when an investor should exit a risky asset in favour of risk free investments. It utilises a 10-month simple moving average to achieve a long term trend following approach across multiple global traditional asset classes.

The trend following approach is compared to a “Buy and Hold” portfolio, with the same 5 asset classes equally weighted.

The trend following portfolio also uses equal weighting and treats each asset class independently, either long the asset class or in cash with its 20% allocation of the funds.

“Figure 13b” of the paper (reproduced below) shows that the trend following portfolio marked as GTAA (Global Tactical Asset Allocation) delivered better performance compared to the “Buy and Hold” portfolio. It also reduces maximum drawdown significantly.

Source: Mebane Faber

The portfolio is tested on various other moving averages lengths and the results are similar, suggesting stability of the parameter and robustness of the strategy. This is detailed in “Figure 15” of the paper (reproduced below).

Source: Mebane Faber

The paper was first published in 2005 and hence performance from 2006 onwards can be considered out of sample. Performance from 2006 and 2012 was as expected with higher risk-adjusted returns and significantly reduced maximum drawdown.

Absolute Momentum Signals Are Similar

The paper “Which Trend is Your Friend?” shows that the two most common and important statistical measures of price trends, namely time series momentum and moving average crossovers, are closely connected. They also capture many other types of trend signals such as HP filter, Kalman filter and all other linear filters.

Absolute Momentum is based on the idea that price trends are more likely to continue than not. The basic strategy is to buy when prices are rising and sell when prices are falling. However finding a price trend among noisy random price moves presents a similar challenge to that of “filtering” information from the noise in many other applications such as astronomy, audio, ballistics, image processing and macroeconomics.

One of the simplest measure of trend is the return over some recent time period, such as returns over the past 12 months. Another simple measure is the moving average crossover method where a shorter term moving average crosses a longer term moving average. The paper shows that the most general form of moving average crossover can be viewed as a special case of the most general time-series momentum using past returns described earlier. Hence using either measures to detect trends would yield similar results. “Table 1” of the paper (reproduced below) shows the similar Sharpe ratio of both Time series momentum and moving average crossover signals using various parameters.

Source: Ari Levine and Lasse Heje Pedersen (AQR Capital Management)

Furthermore the paper shows that other seemingly unique trend filtering techniques such as HP filter and Kalman filter are similar at a higher level. Many generalized forms of trend following strategies would produce similar results.

It is therefore important to focus on the robustness and quality of implementation such as optimally managing transaction costs, dynamic trading, diversification, position sizing, portfolio construction, and risk management.

Combining Absolute and Relative Momentum for Asset Allocation

While Relative Momentum has been researched extensively in academia and remains a robust strategy, it is desirable to be long only when top performers are also in a price uptrend.

Gary Antonacci used a modular approach for portfolio diversification. The modules include Equity, Credit, Real Estate and Economic Stress. Within each module, the indices are subjected to relative strength ranking. The top performing index will be chosen. For example, Credit modules include High Yield and Credit Bonds. Economic Stress modules include Gold and Long-term Treasury. Subsequently the top performer will be compared to Treasury Bills to determine if excess returns are positive or negative. If excess returns are positive, we will invest in the chosen asset. If excess returns are negative, we will invest in Treasury Bills.

“Table 10” of the paper (reproduced below) shows the results of each module and an equally weighted composite of all four dual momentum modules. The composite shows the highest Sharpe Ratio and significantly reduced Maximum Drawdown.

Gary Antonacci explored combining absolute and relative momentum on a few asset classes. Specifically he anchors the portfolio with US stocks and switches into non US stocks using relative momentum. Absolute momentum is applied by comparing the stronger equity index with a risk free rate of return. When the chosen equity index outperforms the risk free rate of return, invest in the chosen equity index. If the chosen equity index underperforms the risk free rate of return, invest in a bond index.

Gary showed us in his book that while both absolute and relative momentum outperforms the relevant benchmark, a combination of absolute and relative momentum produces the best risk-adjusted returns with significant max drawdown reduction.

The strategy of combining absolute and relative momentum proved to be robust with different lookback periods as well as different ways of defining absolute momentum.

Historical Profitability of Absolute Momentum For Last Century

AQR’s paper investigated the performance of Absolute Momentum strategy for the last century (back to 1903).

“Exhibit 1” of the paper (reproduced below) shows the remarkably consistent performance over an extensive time horizon that includes the Great Depression, multiple recessions and expansions, multiple wars, stagflation, the Global Financial Crisis, and periods of rising and falling interest rates, as described by AQR.

While the strategy benefited from the long secular decline in interest rates over the past 30 years, the best performing decade was during the 1973-1982 period, when US 10 year treasury yields rose from 6.4% to 10.4% with extreme volatility in between.

AQR’s long term out-of-sample evidence suggests that it is unlikely that such price trends are a product of statistical randomness or data mining. Trends appear to be a pervasive characteristic of speculative financial markets over the long term.

Source: AQR Capital Management

AQR also looked at the 10 largest drawdowns as shown in “Exhibit 5” of the paper (reproduced below) for the set of returns numbers shown in “Exhibit 1” earlier.

Historical Profitability of Absolute Momentum For Last Two Centuries

Capital Fund Management’s paper explores trend-following strategies across four asset classes (commodities, currencies, stock indexes and bonds) over the last two centuries.

The paper finds that the trend following effect is very stable, across both time and asset classes, making the existence of trends one of the most statistically significant anomalies in financial markets. There is no sign of a statistical degradation of long trends, whereas shorter trends have significantly withered.

The performance is remarkably constant over two centuries. The overall performance is in fact positive over every decade in the sample.

Absolute Momentum Through Different Interest Rate Cycles

Investors are concerned with how investing strategies would behave across different interest rate cycles. PIMCO explored how absolute momentum strategies had performed across different interest rate cycles. Specifically they studied the hypothetical excess returns of a simple absolute momentum strategy with US Equities and 5 year Treasuries across different interest rate cycles. The excess returns are broken out by annual change in 5 year yield over the year.

“Figure 1” from PIMCO’s paper (reproduced below) shows that the simple absolute momentum strategy produced best excess returns in years where the 5 year yield fell 100 bps or more. In rising and range bound interest rate years, absolute momentum produced positive excess returns.

Source: PIMCO

PIMCO also examined the rising interest rate years in further detail as generating positive returns is most challenging in these periods. See “Figure 3” from PIMCO’s paper (reproduced below).

Trend-following returns are typically back-loaded: The model tends to lose money initially upon entering a period of rising rates, but once a new trend is identified, positions switch and may profit. The years 1979, 1994 and 2009 were the exceptions over this sample. In each case, whipsaw in the equity market led to losses.

Source: PIMCO

PIMCO then concludes by saying:

Unanticipated periods of rising rates may have unpredictable results on multi-asset portfolios and on some popular strategies. No strategy can fully mitigate this, but we find that trend-following strategies do have the potential to exhibit fairly robust returns during such episodes thanks to their ability to take short positions in markets that are falling. Trend following, by its nature, tends to miss market turning points, and may lose money initially on spikes in rates or in periods of volatile but range-bound rate moves. However, our analysis shows that over extended periods, trend-following has the potential to perform strongly in all phases of the rates cycle, with contributions to that performance coming from all asset classes.

Strong Performance Of Absolute Momentum During Extreme Events

“Exhibit 2” in AQR’s paper (reproduced below) shows that Absolute Momentum strategy has done well in extreme up or down years for the stock market.

Source: AQR Capital Management

AQR looked at the performance of Absolute Momentum strategy during extreme events in another way. “Exhibit 3” of the paper, reproduced below, shows the performance of Absolute Momentum strategy during the 10 largest drawdowns experienced by the traditional 60-40 portfolio. It is shown that Absolute Momentum strategy experienced positive returns in 9 out of 10 of these stress periods and delivered significant positive returns during a number of these extreme negative stock market events.

Source: AQR Capital Management

Why Does Absolute Momentum strategies perform well during bear markets?

AQR Capital Management argues that majority of bear markets have historically occurred gradually over several months, rather than abruptly over a few days, which allows trend followers an opportunity to position themselves short after the initial market decline and profit from continued market declines. Looking at how Absolute Momentum strategies perform during crisis periods, some investors have the misconception that practitioners (managed futures, global macro hedge funds, etc) employing such strategies predicted the crises and hence profited from shorting Equities. Predicting the exact onset of a market crisis is very hard. Instead, practitioners employing such strategies positioned themselves to react to market movements, diversifying across asset classes and markets, waiting to profit from persistent trends.

Kathryn Kaminski’s paper decomposed Managed Futures returns during crisis periods according to sectors as shown in chart below. It is clear that returns are coming from various sectors and diversification is at work.

Source: Kathryn M Kaminski

In a separate paper, AQR documented the returns of major asset classes during the 10 worst Global Equity quarters, shown in “Exhibit 1” of the paper, reproduced below. Simple Style Composite is a composite of 5 long/short style premia including Value, Momentum, Carry, Defensive and Trend.

Source: AQR Capital Management

The same paper also explored the returns of selected asset classes and premia styles during the 10 worst fixed income quarters, shown in “Exhibit 3” of the paper, reproduced below. We can see that Equities were not good hedges but the long/short styles performed well, including Momentum and Trend.

Source: AQR Capital Management

State Street Global Advisors showed in “Figure 4” of a paper (reproduced below) that Managed Futures funds delivered flat or positive performance during the 15 worst months for the S&P 500 index.

Source: SSGA

What Drives Trends To Persist?

Price trends persist due to behavioral biases of investors such as:

Anchoring: Tendency to overweight the importance of the first information that we learn. People anchor their views to past data and are reluctant to adjust their views to new information. Anchoring leads to inertia which causes investors to underreact to news. Once price trends develop, they remain strong for some time.

Confirmation bias: Tendency to over-emphasize the importance of information that confirms our views. Investors who are subjected to confirmation bias, extrapolating recent price trends, may invest more in assets that have done well recently, causing trends to persist.

Herding and Feedback Trading: Herding has a strong physiological and psychological basis. It is associated with the release of oxytocin and positive feelings of trust and security of being part of a group. Some investors follow positive feedback strategies, leading them to buy securities when prices rise and to sell securities when prices fall, causing price over-reaction and momentum profits.

Disposition Effect: Tendency of investors to sell their winners too early and holding on to losers to long, leading to under-reaction to news events.

The trading activity of non-profit seeking market participants, such as central banks and corporate hedging programs, also drives trends to persist.

Behavioral finance argues that markets are inefficient. While long term trends are typically driven by fundamental drivers, it takes time for market participants to react and for supply and demand factors to be fully reflected in asset prices.

In terms of relative momentum, behavioral finance also suggests that investors are more comfortable buying when price is rising as opposed to buying when price is falling.

Momentum Is Lagging By Design

Trend measurement of a time-series is subjected to a lag by design. The lag depends on the number of observations used for trend measurement. For example, using moving averages to measure trends, the trend over the defined time interval is subject to a delay corresponding to about half of the observations. – “CTAs Which trend is your friend – 1741 asset management“

Combining Absolute and Relative Momentum

Gary Antonacci’s paper explored combining absolute and relative momentum on a few asset classes. Specifically he anchored the portfolio with US stocks and switch into non US stocks using relative momentum. Absolute momentum is applied by comparing the stronger equity index with a risk free rate of return. When the chosen equity index outperforms the risk free rate of return, invest in the chosen equity index. If the chosen equity index underperforms the risk free rate of return, invest in a bond index.

This method of adaptive asset allocation keeps investors in tune with changing market regimes. Gary showed us in his book that while both absolute and relative momentum outperforms the relevant benchmark, a combination of absolute and relative momentum produces the best risk-adjusted returns with significant max drawdown reduction.

The strategy of combining absolute and relative momentum proved to be robust with different look-back periods as well as different ways of defining absolute momentum.

Both absolute and relative momentum can enhance returns but absolute momentum works better in reducing volatility and drawdown. Combining both absolute and relative momentum works the best.

Mebane Faber’s paper begins with 13 traditional asset classes and selects the top six out of the thirteen assets as ranked by an average of 1, 3, 6, and 12-month total returns (momentum). The assets are only included if they are above their long-term moving average, otherwise that portion of the portfolio is moved to cash. Performance is consistent over the last 30 years with Sharpe Ratio at 1.06.

Relative Momentum And Value Investing

Relative Momentum and Value Investing are opposites in various aspects. Relative Momentum is procyclical, works well over a relatively short term period of 1 year and based on trending markets while value investing is contrarian, works well over a relatively longer term period of 5-7 years and is mean reverting. These differences in characteristics made the two strategies complementary.

During strong momentum markets, value investing, which focuses on out-of-favor stocks, has often lagged. Conversely, in mean-reverting markets, momentum investing, which focuses on stocks that have done well recently, typically lags.

Source: Wellington Management

Furthermore AQR shows in the paper: “The Case for Momentum Investing” that adding Relative Momentum to a Value-focused portfolio improves risk-adjusted returns as measured by the Sharpe ratio. See “Exhibit 6” of the paper (reproduced below).

Source: AQR Capital Management

Absolute Momentum and Private Equity

Private equity and trend following strategies have complemented each other well, each performing well when the other performed poorly – AQR. Private Equity and Trend Following returns show slight negative correlation especially in left tail episodes for each. “Exhibit 4” of the paper shows the performance of Private Equity and Trend Following strategies when either is performing poorly.

Source: AQR Capital Management

Convexity of Momentum Strategies

Nassim Taleb explains convexity in his book, “Antifragile”, using a simple concept:

If you lift 100 kilos it is more beneficial than lifting one gram 100 times. If a double dose gets more than twice the response, it is convex. Convex systems like volatility. Concave systems hate it. A system is convex (and by extension anti-fragile) if it has more to gain than to lose from disorder.

Momentum strategies are convex strategies.

“Figure A and B” from Tom Basso’s paper: “The Driving Force Behind Profits in the Managed Futures Industry” (reproduced below) show that the more change a market has, the more profits a portfolio will gain from that market. This observation is consistent across many asset classes. “Figure A” shows S&P 500 while “Figure B” shows Live Cattle.

Source: Tom Basso

Source: Tom Basso

“Figure D” below shows the same observation indicating that changes in price on average for all markets generate more profits for absolute momentum strategies as a whole.

“Exhibit 2” of the paper (reproduced below) shows that Absolute Momentum strategy has done well in extreme up or down years for the stock market.

Source: AQR Capital Management

Skew of Momentum Strategies

Skew is a measure of asymmetry of return distribution.

Positive skew is the ability to have lower volatility than average when losing money and higher volatility when making money. Negative skew is the opposite; it is the characteristic of having higher volatility than average when losing money and lower volatility when making money.

A set of returns made up of frequent small, lower than average, returns and occasional large gains would be positively skewed. Conversely, a set of returns with frequent small, above average, returns and occasional large losses would be negatively skewed.

During their three worst drawdowns, low skew strategies lose 4.2 times their ex-ante (preceding) volatility while high skew strategies lose 2.3 times their ex-ante volatility. For low skew strategies, historical volatility is inadequate for estimating the risk of future loss.

During their three worst drawdowns, the strategies with high Sharpe ratios lose 4.3 times their ex-ante volatility, while the strategies with low Sharpe ratios lose only 2.2 times their preceding volatility.

Combining Absolute Momentum And Carry

When both absolute momentum and carry is positive, returns are significantly better across multiple major asset classes and markets as shown in “Exhibit 6” from PIMCO’s paper (reproduced below).

Conceptually, we can think of carry as a position that harvests risk premiums, and thus, performs best when prices don’t move much, whereas trend-following is a long-tail option-replicating strategy, which benefits when prices move as a consequence of fat-tail events such as those experienced during the financial crisis. Thus, combining these two strategies should intuitively result in better portfolio outcomes in a broad set of states.

Source: Pimco

Quote from PIMCO: “Be on the right side of the trend, and don’t pay too much while you are at it.”

Benefits Of Using Stop Losses

Kathryn Kaminski’s paper found that applying stop losses on momentum strategies generally improves both returns and reduces risk of the portfolio. Losses tend to persist in the presence of momentum and having a stop loss in place can be more profitable than staying fully invested.

Furthermore Modus’ paper analyzed the impact of implementing simple stop loss rules on a daily and weekly trend following portfolio. The paper finds that stop loss rules are most effective in improving maximum drawdowns. Improvements are more effective for the longer term strategies which are naturally prone to severe drawdowns. However average drawdown and the time for recovery from the drawdown do not benefit much from the stop loss rules.

Impact Of Trading Frequency

Modus’ paper explores the impact of trading frequency on trend following strategies. The paper finds:

Contrary to the general expectation that a higher frequency of trading is more beneficial, we find that when applied to the same strategies, daily trading of portfolios does not significantly improve risk and return characteristics of the strategies.

For both daily and weekly portfolios, the strategy with the best risk-adjusted returns are generally the ones with shorter fast moving averages; i.e. 20 and 40 days and their weekly equivalents.

No matter the frequency of trading, the characteristics of the various strategies are not stationary over time and we notice a large degree of variability during the simulation period.

It should be noted that the average correlation between the return streams of daily strategies and their weekly equivalent is over 0.97. As you would expect, the least performing strategies have a slightly lower correlation coefficient though still higher than 0.60 across the board.

Performance Dispersion Of CTAs

Campbell & Company’s research paper: “Return Dispersion, Counterintuitive Correlation” shows that “CTA portfolios capture returns with substantial variation and this variation is more pronounced during periods when momentum strategies are performing strongly.” In other words, “When CTAs perform their best they are the MOST different from one another.”

“Figure 4” from Campbell’s paper (reproduced below), shows that when return dispersion is high, average return is high.

Figure 4: Return dispersion (standard deviation across managers in the Newedge Trend index) vs. average return (sample average across managers in the Newedge Trend index) from 2000-2014. Performance data is used for 7 of 10 Newedge Trend Index constituents due to data availability. All returns are risk adjusted to 4 percent monthly. Source: Stark & Company. Chart from Campbell & Company.

When performance is very high, return dispersion tends to be high for CTAs. This implies a breakdown in correlation between managers. Intuitively this suggests that under normal scenarios with moderate opportunities for CTAs, subtle differences in system construction, parameter selection, and risk management seem to be less important.

“Figure 8” from the same paper, reproduced below, shows that “CTAs can be markedly dissimilar when correlation breaks down”